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Renewal-Theoretical Dynamic Spectrum Access in Cognitive Radio Networks with Unknown Primary Behavior

Chunxiao Jiang, Yan Chen, K. J. Ray Liu, Yong Ren

arXiv:1111.4969v1cs.NI

TL;DR

The paper studies interference when secondary users access a primary channel without knowing the primary user’s exact communication mechanism. It proposes a dynamic access protocol, proves renewal behavior, derives closed-form interference quantities, and optimizes secondary access under primary QoS and secondary stability constraints.

  • Problem

    Unknown primary behavior can cause additional interference when secondary users transmit without knowing when primary communication will recur.

  • Method

    The paper proposes a dynamic spectrum access protocol and analyzes secondary communication behavior in an ON-OFF primary channel using Renewal Theory.

  • Results

    The analysis proves that secondary communication behavior is a renewal process and derives closed-form expressions for the interference quantity.

  • Takeaways & Limitations

    Secondary arrival rate and transmission time can be optimized to control primary interference while maintaining secondary-network stability.

Abstract

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Dynamic spectrum access in cognitive radio networks can greatly improve the spectrum utilization efficiency. Nevertheless, interference may be introduced to the Primary User (PU) when the Secondary Users (SUs) dynamically utilize the PU's licensed channels. If the SUs can be synchronous with the PU's time slots, the interference is mainly due to their imperfect spectrum sensing of the primary channel. However, if the SUs have no knowledge about the PU's exact communication mechanism, additional interference may occur. In this paper, we propose a dynamic spectrum access protocol for the SUs confronting with unknown primary behavior and study the interference caused by their dynamic access. Through analyzing the SUs' dynamic behavior in the primary channel which is modeled as an ON-OFF process, we prove that the SUs' communication behavior is a renewal process. Based on the Renewal Theory, we quantify the interference caused by the SUs and derive the corresponding close-form expressions. With the interference analysis, we study how to optimize the SUs' performance under the constraints of the PU's communication quality of service (QoS) and the secondary network's stability. Finally, simulation results are shown to verify the effectiveness of our analysis.

I. INTRODUCTION

The paper addresses interference from secondary users with unknown primary behavior by analyzing dynamic access at the MAC layer. It proposes a renewal-theoretic protocol and optimization framework balancing secondary throughput, primary QoS, and network stability.

  • Dynamic spectrum access improves spectrum utilization but can cause adverse interference to primary-user communication.
  • Traditional interference models often aggregate secondary transmission power and path-fading effects without modeling primary and secondary communication behaviors.
  • The paper proposes a dynamic access protocol for secondary users lacking knowledge of the primary network’s exact communication mechanism.
  • It quantifies MAC-layer interference as the proportion of primary communication periods interfered by secondary dynamic access, rather than aggregated physical-layer signal power.
  • Renewal Theory yields closed-form interference expressions after proving that secondary communication behavior in the primary channel is a renewal process.
  • The paper formulates secondary access control as maximizing average data rate subject to primary QoS and secondary-network stability constraints.

II. SYSTEM MODEL

The system consists of a primary user and coordinated secondary users sharing one primary channel whose communication mechanism is private. The channel alternates between ON and OFF states, while a coordinator manages opportunistic secondary access.

  • The network contains one primary user and M secondary users operating on one channel, with primary access having priority.
  • Secondary users may access the channel opportunistically only while preserving the primary user’s communication QoS.
  • The primary communication mechanism is private, so secondary users do not know when primary communication will arrive and cannot synchronize to primary time slots.
  • A coordinator observes primary-channel behavior, determines availability, and coordinates secondary access through a control channel.
  • The primary channel alternates between ON occupancy and OFF spectrum-hole states, with ON and OFF durations modeled as independent exponential random variables.
  • The protocol uses FIFO request handling, immediate transmission for duration Tt after confirmation, coordinator sensing, and request-frequency limits.

B. Queuing Model

The secondary network is modeled as a queue whose access-generated transmissions interact with the ON-OFF primary channel. The paper defines MAC-layer interference and explains why unknown primary recurrence creates additional interference.

  • B. Queuing Model: Requests from all secondary users arrive at the coordinator through a Poisson process, giving exponential request-arrival intervals with expectation λs.
  • B. Queuing Model: The coordinator buffer stores request order, while packets remain in each secondary user’s data memory and the modeled buffer is effectively infinite.
  • B. Queuing Model: Each secondary user’s service time includes transmission time Tt and waiting associated with the primary channel’s ON state.
  • B. Queuing Model: The protocol repeatedly senses the primary channel and confirms the queued request at the head of the FIFO list when the channel is OFF.
  • Interference Quantity: Because half-duplex secondary users cannot receive coordinator commands during transmission, they may miss primary recurrence and create additional interference.
  • Interference Quantity: The interference quantity QI is the proportion of accumulated interference periods to the total duration of primary ON states.

IV. INTERFERENCE CAUSED BY SUS WITH ZERO ARRIVAL INTERVAL

With λs = 0, the SUs continuously have packets to transmit, creating a worst-case interference scenario for the PU. Their transmission-and-waiting behavior forms a renewal process, allowing interference to be analyzed through Renewal Theory.

  • λs = 0 means the coordinator always has transmission requests, so the SUs continuously seek access to the primary channel.This is described as the worst case because it considers maximum interference from the SUs.
  • The SUs alternate between transmitting one packet and waiting for the primary channel’s OFF state.Waiting occurs when the previous transmission ends during the PU’s ON state.
  • Interference to the PU occurs only during SU transmission time Tt, so its quantity depends on the occurrence probability of Tt.The analysis therefore focuses on the SUs’ communication behavior during packet transmissions.
  • The interval Tb between adjacent transmission beginnings satisfies Tb = Tt + Tw and is a renewal process when the intervals are positive i.i.d. random variables.Because Tt is fixed, the proof establishes that the waiting times Tw are i.i.d.
  • The waiting time Tw is zero when transmission ends in the OFF state and otherwise equals the forward recurrence time of the PU’s ON state.All waiting times are shown to be identically distributed and independent, making the transmission intervals i.i.d. as well.
  • The SUs’ communication behavior is a renewal process, and the paper defines I(t) as expected accumulated interference to the PU over time t.The interference analysis derives expressions for the interference generated during Tt and the associated waiting time.

1) Expected interference I(Tt):

The paper models expected interference I(t) over intervals beginning in the PU’s OFF state while SUs transmit continuously. Renewal equations, Laplace transforms, and inverse transforms yield a closed-form expression for I(t).

  • Expected interference I(Tt): The expected interference function I(t) satisfies a renewal equation based on the PU’s renewal interval density fp(t) and cumulative distribution Fp(t).The first OFF and ON states are modeled as independent, supporting the recursive formulation.
  • Expected interference I(Tt): Laplace transforms are applied to the renewal equation by decomposing I(t) into three terms, followed by an inverse Laplace transform.The transformed components I1(s), I2(s), and I3(s) correspond to the three terms in the decomposition.
  • Expected interference I(Tt): Theorem 2 identifies the renewal characteristic of I(t) and provides its Laplace-transform representation.Substituting the specified PU renewal distributions enables calculation of the transform.
  • Expected interference I(Tt): The inverse Laplace transform produces a closed-form expression for I(t).This expression is obtained from the transformed representation derived in the preceding steps.

2) Expected waiting time E(Tw):

The expected waiting time E(Tw) is derived from the probability that an interval starts in the PU’s OFF state and ends in its ON state. Closed-form expressions then determine E(Tw) and the interference quantity QI1.

  • Expected waiting time E(Tw): PON(t) is the average probability that a period starts in the OFF state and ends in the ON state.This probability is used to characterize when SUs must wait for the PU’s OFF state.
  • Expected waiting time E(Tw): The expected waiting time E(Tw) is expressed using PON(Tt) and the forward recurrence time of the PU’s ON state.The derivation separately obtains closed-form expressions for PON(Tt) and E(bTON).
  • Expected waiting time E(Tw): PON(t) is obtained by solving its renewal equation through Laplace and inverse Laplace transforms.Theorem 3 supplies the renewal-equation formulation used in this derivation.
  • Expected waiting time E(Tw): For Poisson-distributed PU ON states, Renewal Theory determines the forward recurrence-time quantity used in the waiting-time calculation.Combining the resulting expressions yields the SUs’ average waiting time.
  • Expected waiting time E(Tw): Substituting the expected interference and waiting-time expressions yields the interference quantity QI1.This calculation applies to the zero-arrival-interval case analyzed in the preceding section.

A. SUs’ Communication Behavior Analysis

When SU requests arrive with a nonzero Poisson arrival interval, SU behavior alternates between idle and busy states. The paper proves that these cycles are i.i.d., making the overall communication behavior a renewal process.

  • SUs’ Communication Behavior Analysis: With λs ≠ 0, the coordinator’s buffer may become empty, introducing an idle state in addition to the busy state.The analysis first studies this idle-busy communication behavior and then quantifies its PU interference.
  • SUs’ Communication Behavior Analysis: The SU behavior switches between idle and busy states, analogous to the PU’s ON-OFF model.The paper specifically studies whether this idle-busy switching is itself a renewal process.
  • SUs’ Communication Behavior Analysis: Idle-state lengths are forward recurrence times of SU arrival intervals and are i.i.d. because requests arrive according to a Poisson process.The idle-state duration is denoted TI.
  • SUs’ Communication Behavior Analysis: Busy-state lengths are constructed from N SU transmitting-waiting times, whose distribution is analyzed through the embedded Markov process of buffer states.The number N is shown to be identically distributed and independent across busy states.
  • SUs’ Communication Behavior Analysis: The cycle length Tc = TI + TB is i.i.d. because idle and busy-state lengths are independently i.i.d.Consequently, the sequence of SU communication cycles forms a renewal process.

B. Interference Quantity Analysis

The paper models the secondary network and primary channel as a single-server queue to derive interference quantities and formulate optimization under PU QoS and secondary-network stability constraints.

  • Interference modeling: The system models SU data packets as customers and the primary channel as the single server in an M/G/1 queuing system.An SU service time combines its transmission time Tt and the next SU’s waiting time Tw.
  • Interference modeling: ρ represents the proportion of time that the coordinator is busy, equivalently the probability that an SU packet occupies the server.The system allows at most one SU packet in the server.
  • Optimization formulation: The optimization chooses SU packet arrival interval λs and transmission time Tt to maximize average SU data rate while limiting interference and preserving stability.The PU average data rate must be at least R↓ p, and the secondary-network stability condition must hold.
  • PU QoS constraint: The PU average data rate is calculated from interference periods relative to the PU’s overall communication time, with PU rates differing between interference and no-interference periods.QI2 denotes the ratio of interference periods to the PU’s overall communication time.
  • Stability constraint: The stability evaluation considers λs ≠ 0 and derives the secondary-network constraint from the single-server queue model.The stability condition is based on the queueing-system analysis introduced for the secondary network and primary channel.

2) SUs’ Stability Condition:

The paper derives the secondary-network stability condition from a single-server queue and characterizes how SU performance and the constraints vary with Tt and λs.

  • SUs’ Stability Condition: For Poisson SU packet arrivals, secondary-network stability requires the server load to satisfy ρ < 1.The secondary network and primary channel are modeled as a single-server queuing system.
  • SUs’ Stability Condition: The stability condition function S(Tt, λs) is derived to represent the secondary network’s stability constraint.The resulting function is used in the optimization problem alongside the PU QoS constraint.
  • Monotonicity results: The SUs’ average data rate strictly increases with transmission time Tt and strictly decreases with average arrival interval λs.These monotonicities are stated in Theorem 5.
  • Monotonicity results: The PU’s average data rate and the stability condition function are strictly decreasing in Tt and λs.Theorem 5 states these monotonic relationships for the optimization variables.
  • Optimization solution: Because the objective and constraints are monotonic in Tt and λs, the optimization solution can be found using gradient-based methods.The paper states this consequence after Theorem 5.

VII. SIMULATION RESULTS

Simulations compare theoretical and simulated interference, queue stability, and average data rates while varying SU transmission time and packet arrival interval.

  • Interference validation: The simulations use an ON-OFF primary channel with λ0 = 2.6s and λ1 = 3.6s, implemented through a Matlab queueing system.The queueing system simulates PU and SU behavior.
  • Interference validation: Simulated QI1 and QI2 converge to their corresponding theoretical results after initial fluctuations, validating the closed-form interference expressions.The expressions are given in (28) and (40).
  • Interference behavior: QI2 is less than QI1 under the same condition because the SU idle state reduces the fraction of time producing interference.The simulations also report increasing interference as SU transmission time Tt increases.
  • Stability validation: With Tt = 0.6s, λs must exceed 1.25s to ensure secondary-network stability; λs = 1.3s remains stable, whereas λs = 1.2s is unstable.The queue length remains bounded in the stable case and eventually diverges in the unstable case.
  • Average data rates: PU average data rate decreases with Tt and increases with λs, while SU average data rate increases with Tt and decreases with λs.These simulations agree with the monotonicity stated in Theorem 5.
  • Optimization results: For λs = 1.3s, the optimal SU average data rate reaches around 0.6bps/Hz under the PU QoS and stability constraints.The feasible transmission time is restricted by the constraint boundaries.
  • Design implication: SU communication behavior should be adjusted dynamically according to the estimated channel parameters λ0 and λ1.These parameters determine the relevant operating conditions for the communication behavior.

VIII. CONCLUSION

The paper models SUs’ communication behavior in an ON-OFF primary channel as a renewal process, derives closed-form interference quantities, and uses them to study secondary-network operation under PU QoS and stability constraints.

  • The SUs’ communication behavior in the ON-OFF primary channel is a renewal process.
  • Closed-form expressions quantify the interference quantity caused by SUs’ dynamic access.
  • The analysis studies how to optimize SUs’ arrival rate and transmission time while controlling PU interference and maintaining secondary-network stability.
  • Simulation results validate the closed-form interference expressions.
  • The derived expressions can evaluate SU interference when configuring a practical secondary network.
  • Future work will study how to concretely coordinate primary spectrum sharing behavior.
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